## What would you do if you become principal of your school?

If I become a principal I would stop these long lectures of discipline and hard work. I would tell students short stories with a moral in them so they could learn good values. I would promote a little more or different extra-curricular activities. I would also decrease the amount of homework.

**What are the ideals of Z?**

The ideals of Z must be subgroups, and the only additive subgroups of Z are those generated by any given element of Z, i.e. for each n∈Z there is a subgroup (n) whose elements are the multiples of n, and in fact these exhaust all possible subgroups.

**What is a school principal job description?**

School principal job description As the principal, you are the face of the school. You’ll lead teachers and staff, set goals and ensure students meet their learning objectives. Overseeing your school’s day-to-day operations means handling disciplinary matters, managing a budget and hiring teachers and other personnel.

### Do ideals contain 0?

An ideal always contains the additive identity 0, as by definition it is an additive subgroup of the additive group structure in the ring. may or may not have an identity element, namely the multiplicative identity 1. If the ring does have 1 and the ideal contains 1, then necessarily the ideal is the entire ring.

**How many ideals does Z12 Z12 have?**

since 7*7 = 1 (mod 12), (7) = Z12. now we also have (3) = {0,3,6,9}. note that 9+9+9 = 3 (mod 12), so (9) contains (3), and of course 9 is in (3), so (3) contains (9)….Deveno.

Similar Math Discussions | Math Forum | Date |
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Confusion about definition of multichains of order ideals. | Number Theory | Jan 12, 2021 |

**How many ideals of Z 12Z are there?**

We also have seen that if an ideal contains a unit, the ideal must be the entire ring. Therefore, the ideals 〈1〉, 〈5〉, 〈7〉, and 〈11〉 are all Page 2 2 equal to Z/12Z. We also have the ideals: 〈2〉 = {0,2,4,6,8,10}, 〈3〉 = {0,3,6,9}, 〈4〉 = {0,4,8}, 〈6〉 = {0,6}, 〈8〉 = {0,4,8} = 〈4〉, 〈10〉 = {0,2,4,6,8,10} = 〈2〉.

## What should a new principal do first?

For Principals: Planning the First Year

- TRANSITION. However possible, transition into your new position before your first day.
- BUILD RELATIONSHIPS. The fundamental pillars of school leadership are relationships; nothing substitutes for building and nurturing them.
- LEARN THE CULTURE.
- DON’T CHANGE EVERYTHING.
- HONOR TEACHERS.
- PICK YOUR BATTLES.
- DELEGATE.
- STAY A WHILE.

**Are prime ideals principal?**

Every prime ideal is principal implies every ideal is principal. In particular, if there exist non-principal ideals, there exists an ideal maximal with respect to being non-principal. If there exists an ideal maximal with respect to being non-principal, it must be a prime ideal.

**Why do you want to become a school principal?**

The role of a principal allows me to spread my reach further and touch more lives than I did as a teacher. When I first started my teaching career, I was content with being a classroom teacher for my entire career. Even in my role, I find time to be in the classroom engaging with students while they learn.

### How do you find the Z12 ideals?

For R = Z12, two maximal ideals are M1 = {0,2,4,6,8,10} and M2 = {0,3,6,9}. Two other ideals which are not maximal are {0,4,8} and {0,6}.

**What are ideals in math?**

An ideal is a subset of elements in a ring that forms an additive group and has the property that, whenever belongs to and belongs to , then and belong to . For example, the set of even integers is an ideal in the ring of integers . Given an ideal , it is possible to define a quotient ring.

**What are examples of ideals?**

The definition of an ideal is a person or thing that is thought of as perfect for something. An example of ideal is a home with three bedrooms to house a family with two parents and two children. Ideal is defined as something or someone who is thought of as a perfect example of something.

## What is an ideal?

1 : a standard of perfection, beauty, or excellence. 2 : one regarded as exemplifying an ideal and often taken as a model for imitation. 3 : an ultimate object or aim of endeavor : goal.

**What are the elements of Z12?**

(c) In the group Z12, the elements 1, 5, 7, 11 have order 12. The elements 2, 10 have order six.

**What are the ideals of a field?**

If R has exactly two ideals, then firstly R≠{0}, so these ideals are precisely R and {0}. Then for any a∈R∖{0}, the ideal aR it generates is not {0} so it must be R. In particular 1∈aR and a is invertible; this holds for any nonzero a so R is a field. If R has an ideal I with I≠{0} and I≠R, then 1∉I (otherwise a=1.

### What is Z12 math?

Z12 = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} in which addition/subtraction and multiplication are carried out mod- ulo 12 (clock face math) Under modulo 12 arithmetic if an operation yields a number larger than twelve, then divide by twelve and retain the remainder as your answer.

**How do you welcome the principal?**

It is a matter of great pleasure and honor for me to welcome the new principal of (School/Institute name), (Principle name). He has previously worked for 5/10 years (More/less) at (School/Institute name) as principal (Job Designation) and has remained successful in delivering positive results. (Describe in your words).

**Are prime ideals maximal?**

Any primitive ideal is prime. As with commutative rings, maximal ideals are prime, and also prime ideals contain minimal prime ideals. A ring is a prime ring if and only if the zero ideal is a prime ideal, and moreover a ring is a domain if and only if the zero ideal is a completely prime ideal.

## What is the importance of a principal?

While principals are most often held accountable for the smooth functioning of routine activities, their most important role is that of instructional leader. The principal is the leader of the school and sets the tone for the school. Their impact is significant.

**How many ideals every field have?**

2 ideals

**How many subgroups does Z12 have?**

Z24 is cyclic, there is exactly one subgroup for any divisor d of 24. The divisors are 1,2,3,4,6,8,12,24, so the answer is eight subgroups. a#b = b ∗ a, for all a, b ∈ S. therefore # is commutative b.

### How do you show an ideal principal?

Definition: Let be a commutative ring. An ideal of the form $aR = \{ a * r : r \in R \}$ is called a Principal Ideal generated by . It is easy to verify that if is a commutative ring then for every , is indeed an ideal of .

**Are ideals rings?**

In general, an ideal is a ring without unity – i.e. without a multiplicative identity – even if the ring it is an ideal of has unity. But the only way the ideal can have the same multiplicative identity – and so be a sub-ring-with-identity – is if it is the whole ring.

**How do you find maximal ideals?**

Given a ring R and a proper ideal I of R (that is I ≠ R), I is a maximal ideal of R if any of the following equivalent conditions hold: There exists no other proper ideal J of R so that I ⊊ J. For any ideal J with I ⊆ J, either J = I or J = R.